Probably to maintain the illusion that they were anti-Voldemort.
Remember that Harry told Cornelius Fudge that Crabbe and Goyle's fathers were Death Eaters.
"Look, I saw Voldemort come back!" Harry shouted. He tried to get out of bed again, but Mrs Weasley forced him back. "I saw the Death Eaters! I can give you their names! Lucius Malfoy -"
Snape made a sudden movement, but as Harry looked at him, Snape's eyes flew back to Fudge.
"Malfoy was cleared!" said Fudge, visibly affronted. "A very old family - donations to excellent causes-"
"Macnair!" Harry continued.
"Also cleared! Now working for the Ministry!"
"Avery - Nott - Crabbe - Goyle -"
(Goblet of Fire, Chapter 36, The Parting of the Ways).
When the Ministry finally accepted that Voldemort had returned they would probably have tried to gather as much information about potential Death Eaters as possible. Through speaking to Fudge or through reading Harry's Rita Skeeter article they would have gathered that Crabbe Senior and Goyle Senior were Death Eaters.
If these families are being watched by the Ministry, what kind of signal does it send out if the kids fail Defence Against the Dark Arts? Death Eaters like Lucius Malfoy were well aware of the need to keep up appearances. He made sure Draco knew that it didn't look good to sound overly unenthusiastic about Harry Potter in public.
"Harry Potter got a Nimbus Two Thousand last year. Special permission from Dumbledore so he could play for Gryffindor. He's not even that good, it's just because he's famous...famous for having a stupid scar on his forehead..."
Malfoy bent down to examine a shelf full of skulls.
"...everyone thinks he's so smart, wonderful Potter with his scar and broomstick-"
"You have told me this at least a dozen times already," said Mr Malfoy, with a quelling look at his son, "and I would remind you that it is not - prudent - to appear less than fond of Harry Potter, not when most of our kind regard him as the hero who made the Dark Lord disappear..."
(Chamber of Secrets, Chapter 4, At Flourish and Blotts).
The Death Eaters may be more powerful at this stage than they once were but they are still an underground movement whose members are vulnerable to arrest. Any suggestion that Crabbe and Goyle are into the Dark Arts or are disinterested in fighting them may put their families in danger. Hence they retook the year to burnish their anti-Voldemort credentials.
This essentially boils down to 'parental pressure'. I doubt that Crabbe and Goyle themselves had much appetite for further learning.
Of course, the real reason why Crabbe and Goyle failed Defence Against the Dark Arts was because of stupidity, not any great ideological crusade. They probably didn't get many O.W.L.s at all in other subjects, either. But those failing those other subjects wouldn't arouse suspicion, which is why Defence Against the Dark Arts was the only subject which we know they retook.